496 (number)
In mathematics, 496 is a natural number following 495 and preceding 497. It is a perfect number, meaning that it is equal to the sum of its proper divisors (divisors excluding the number itself). These proper divisors are 1, 2, 4, 8, 16, 31, 62, 124, and 248, and their sum is 1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248 = 496.
496 is the third perfect number. The first two are 6 and 28. Perfect numbers are relatively rare; the next perfect number after 496 is 8128.
Perfect numbers are closely related to Mersenne primes. A Mersenne prime is a prime number of the form 2p - 1, where p is also a prime number. If 2p - 1 is a Mersenne prime, then 2p-1(2p - 1) is a perfect number. In the case of 496, it is derived from the Mersenne prime 31 (which is 25 - 1), as 496 = 24(25 - 1) = 16 * 31.
496 is also a triangular number. A triangular number is a number that can be represented as the sum of the consecutive natural numbers starting from 1. In this case, 496 is the 31st triangular number, meaning it is the sum of the numbers from 1 to 31: 1 + 2 + 3 + ... + 31 = 496.
Triangular numbers are calculated using the formula n(n+1)/2. For 496, this is 31(31+1)/2 = 31*32/2 = 496.